STRAND E: Data Analysis E2 Data Presentation Text Contents Section E2.1 Pie Charts E2.2 Line Graphs E2.3 Stem and Leaf Plots E2.4 Graphs: Histograms E2. * Histograms with Unequal Class Intervals
E2 Data Presentation E2.1 Pie Charts Pie charts, which represent quantities as sectors of a circle, can be used to illustrate data. They are particularly effective if there is only a small number of items to illustrate. In total a complete circle, i.e. 36, must always be used. Worked Example 1 Tracey uses her pocket money of 18 per month in the following way. Books 4 Sweets 3 Sport 6 Transport 4 Savings 1 Draw a pie chart to show how Tracey uses her pocket money. Solution Tracey has a total of 18. 36 = 2 18 So 2 should be used for each 1. The angles needed are given in this list. Books 4 2 = 8 Sweets 3 2 = 6 Sport 6 2 = 12 Transport 4 2 = 8 Savings 1 2 = 2 Alternatively, you could calculate each angle by taking the appropriate fraction of 36. For example, for Books, we have and for Sweets, The pie chart can now be drawn. 3 18 4 18 36 = 8 36 = 6, etc. 1
E2.1 The diagram below, on the left, shows the first section for 'Books'. The completed pie chart is on the right. Books Transport Savings 2 Books 8 8 12 8 6 Sweets Sports Worked Example 2 The pie chart was constructed after asking 72 students how they travel to school. How many of these students travel to school by: (i) car, (ii) bus, (iii) taxi? What percentage walk to school? Solution There are 72 students so 36 = per student 72 (i) The angle for travelling by car is 4. 4 = 8 So 8 students travel by car. Bus Route Taxi 11 2 4 Car 19 Walk (ii) The angle for travelling by bus is 2. 2 = 4 So 4 students travel by bus. (iii) The angle for travelling by taxi is 11. 11 = 22 So 22 students travel by taxi. 2
E2.1 Note The number who walk to school is given by so the percentage who walk is 38 72 19 = 38 1 2.8% Alternatively, you could just use the angles in the pie chart to give 19 1 2.8% 36 Worked Example 3 The pie chart below, not drawn to scale, shows the Saturday morning activities of a group of 12 children. Swimming x 1 Dance Soccer (i) The sector for soccer is represented by an angle of 1. Determine the number of children who play soccer on Saturday mornings. (ii) Given that 46 children swim on Saturday mornings, calculate the value of x. (iii) Determine the probability that a child chosen at random, dances on Saturday mornings. Solution (i) Number playing soccer = 1 36 12 = children (ii) Angle for swimming = 46 12 = 138 36 (iii) Number dancing = 12 ( + 46) = 12 96 = 24 So probability of dancing = 24 = 12 (Probability is covered in detail in Strand D.) 1 3
E2.1 Exercises 1. In an opinion poll 36 people were asked who they would vote for in the next election. Their responses were: Conservative 16 Labour 17 Liberal Democrat 2 UKIP 1 Draw a pie chart to show this. 2. Bethany recorded how she spent the last 24 hours. Her results are shown below. Sleeping 9 hours School 7 hours Homework 2 hours Watching TV 3 hours Eating 1 hour Travelling 2 hours Draw a pie chart to show this information. 3. A student estimated that he had 3 hours available each week for home study and for sports. The table below shows the percentage of time he spent on each activity. Activities % Languages 3 Mathematics 2 Computer Studies 1 Sciences 1 Sports x (c) (d) Calculate the number of hours he spent on sports. Calculate the angles in a pie chart that would be used to represent the hours spent on (i) Mathematics (ii) Languages. Draw a pie chart to represent the distribution of hours in the week, which the student spends on the activities indicated in the table above. One hour in the 3 hours is chosen at random. Calculate the probability that the student is (i) playing sports (ii) studying Mathematics or Languages. 4
E2.1 4. The 3 students in a class state their favourite sport. Their results are listed below. Basketball 3 Cricket 9 Athletics 6 Netball 2 Football 1 Draw a pie chart to show this information. BBC One. The pie chart shows how the time Robert spends watching television is split between different channels, for one day. Ron spends 1 hour watching BBC One. ITV2 How long does he spend watching ITV2? How long does he spend watching Sky Sports? 9 4 22 6. Andrew was given 6 on his birthday. The pie chart shows how he spent this money. How much did he spend on: cinema tickets, (c) his new jeans, sports equipment? Sports equipment 21 Cinema tickets 6 9 Sky Sports New jeans 7. The pie chart shows the football teams supported by a class of students. There are 3 students who support Harbour View. Tivoli Gardens Portmore United Harbour View 36 72 16 Boys Town
E2.1 (c) (d) What is the angle representing Tivoli Gardens? How many students support Boys Town? How many students are there in the class? How many students support Portmore United? 8. A Post Office in a village dealt with 72 letters in one week. They were sorted into First Class, Second Class and Air Mail. The pie chart shows the different number of each type. How many letters of each type were handled? 9. Kelly spent 9. The table shows what she spent it on. Second Class 17 First 16 Class 2 Air Mail Items Bus fares Going out Clothes DVDs Other Amount spent 12 2 3 1 8 Total Spending 9 Kelly is asked to construct a pie chart to show her spending. Work out the angle of each sector in the pie chart. Items Angle of sector Bus fares Going out Clothes DVDs Other Total of angles 36 (c) Construct the pie chart to illustrate the data. What fraction of Kelly's spending was on clothes? 6
E2.1 1. Andrew spends 18 per week. The way in which he spends his money is shown in the table. Items Spending ( ) Food Heating and lighting Clothes Other items Housing 3 12 2 2 98 Total Spending 18 Draw a pie chart to show how Andrew spends his money. This pie chart shows how the average person spends money. Other items Food Clothes Housing Heating and lighting Describe one way in which Andrew's spending differs from the average person's spending. 11. This question is about the way water is used in two Mozambique villages. In village A, 324 litres of water are used each day. The pie chart shows how the water is used. Cooking Given to animals 9 4 4 Washing pots Washing themselves 9 72 Washing clothes (i) (ii) How much water (in litres) is used each day for cooking? What fraction of the water used is given to animals? 7
E2.1 In village B, the water is used as follows: Cooking 2% Washing themselves % Washing clothes 2% Washing pots 1% Represent this information in a pie chart. E2.2 Line Graphs A line graph is drawn by plotting data points and joining them with straight lines. It is really only the actual data points that count, but by drawing the lines you get a better impression of the trend in the data points. This method of representation is particularly useful when illustrating trends over time. Worked Example 1 Samuel recorded the temperature in his shed at 6 am each day for a week. His records are shown on this line graph. 3 2 2 Temperature ( C) 1 1 M T W T F S S Day (c) What was the temperature on Wednesday? What was the lowest temperature recorded? What was the highest temperature recorded? 8
E2.2 Solution For Wednesday the temperature can be read as 2 C. 3 2 C 2 Temperature ( C) 2 1 1 M T W T F S S Day The lowest temperature occurred on Friday and was 19 C. (c) The highest temperature occurred on Sunday and was 3 C. 3 C 3 Temperature C 2 2 1 19 C 1 M T W T F S S Day Worked Example 2 As part of a science project Evan records the height of a plant every week. His results are shown in this table. Week Height (cm) 1 2 3 4 6 1 3 4 6 8 9 Draw a line graph to show the data. Solution First draw a suitable set of axes. Then plot a point for each measurement as shown on the following graph. 9
E2.2 9 8 Week 6, Height 9 Week, Height 8 Height (cm) 7 6 4 Week 4, Height 6 Week 3, Height 4 3 Week 2, Height 3 2 1 Week 1, Height 1 Week, Height 1 2 3 4 6 Week The points can then be joined with straight lines as shown in the next graph. 9 8 7 6 Height (cm) 4 3 2 1 1 2 3 4 6 Week 1
E2.2 Exercises 1. The line graph shows the monthly rainfall for a town. 8 7 6 Rainfall (cm) 4 3 2 1 (c) (d) J F M A M J J A S O N D Month How much rain was there in September? In which month was the rainfall cm? Which months were the wettest? Which months were the driest? 2. Paul recorded the temperature outside his house in New York at 8. am every day. His results are in the table. Day Temperature ( C) M T W T F S S 8 4 6 7 3 Draw a line graph for this data. 3. Annie counted the number of cars that drove past her while she was waiting at the bus stop each morning on her way to work. Day Number of cars M T W T F S 18 12 22 36 4 1 Draw a line graph for this data. 11
E2.2 4. A mug was filled with hot water and the temperature was recorded every minutes. The graph below shows the results. 8 7 6 Temperature ( C) 4 3 2 1 1 1 2 2 3 3 4 Time (mins) What was the temperature after 2 minutes? What was the temperature at the start of the experiment? (c) When was the temperature 4 C? (d) How long did it take for the temperature to drop from 68 C to 36 C?. Anna recorded the time it took her to walk to school every day for a week. Day M T W T F Time taken (mins) 8 9 1 12 7 Draw a line graph for this data. 6. The following graph shows how the height of a sunflower plant changed in the weeks after it was planted in a garden. (c) (d) What was the height of the plant when it was planted in the garden? How much did the plant grow in the first week? What is the greatest height that the graph shows? How long did it take for the height to increase from 4 cm to 78 cm? 12
E2.2 8 7 6 Height (cm) 4 3 2 1 1 2 3 4 6 7 Weeks E2.3 Stem and Leaf Plots There are many ways of representing data. For example, you should already be familiar with histograms and pie charts but there is another very simple way which quickly gives an overall view of the general characteristics of the data. This is called a stem and leaf plot and the following example illustrates how it works. Suppose the marks gained out of by 1 pupils in a Biology test are as given below. 27 36 24 17 3 18 23 2 34 2 41 18 22 24 42 We form a stem and leaf plot by recording the marks with the 'tens' as the stem and the 'units' as the leaf, as shown opposite. The leaf part is then reordered to give a final plot as shown. This gives at a glance both an impression of the spread of the numbers and an indication of the average. Stem Leaf 1 7 8 8 2 7 4 3 2 4 3 6 4 4 1 2 Stem Leaf 1 7 8 8 2 2 3 4 4 7 3 4 6 4 1 2 13
E2.3 Worked Example 1 Form a stem and leaf plot for the following data. 21 7 9 22 17 1 31 17 22 19 18 23 1 17 18 21 9 16 22 17 19 21 2 Solution Without reordering we have, and reordering, Stem Stem Leaf 7 9 9 1 7 7 9 8 7 8 6 7 9 2 1 2 2 3 1 2 1 3 1 Leaf Worked Example 2 7 9 9 1 6 7 7 7 7 8 8 9 9 2 1 1 1 2 2 2 3 3 1 Blood samples were taken from forty blood donors and the lead concentration (in mg per 1 ml) in each sample was determined. The results are given below. 39 24 19 31 6 3 2 17 3 28 2 3 6 22 31 44 24 38 18 18 36 64 43 2 23 28 2 42 3 4 2 24 41 4 3 32 28 3 17 28 (c) Construct a stem and leaf diagram to represent these data. For these data, write down the values of (i) the range, (ii) the median. Describe the shape of the distribution. Solution Reading from the table, Stem Leaf 1 9 7 8 8 7 2 4 8 2 4 3 8 4 8 8 3 9 1 1 8 6 2 4 4 3 2 1 3 3 6 4 14
E2.3 and, reordering, Stem Leaf 1 7 7 8 8 9 2 2 3 4 4 4 8 8 8 8 3 1 1 2 6 8 9 4 1 2 3 4 3 3 6 4 (i) The range is 6 17 = 48 (ii) Using these 4 data values, the median is the 1 2 i.e. the average of the 2th and 21st values. This is 1 2 ( 4 + 1 ) = 2. th, ( 3 + 3 ) = 3. Exercises 1. Ten pupils took the following times in minutes to get to school: 12 7 14 23 11 18 1 8 11 Draw an ordered stem and leaf diagram to show this information. Key: 1 2 represents 12 minutes............ 2. The stem and leaf diagram shows the amounts that 1 pupils spend on healthy food. Key: 3 means 3 pence 3 9 4 8 8 1 6 8 9 6 8 7 (c) What is the range of the amounts spent? What is the median of the amounts spent? What is the mode of the amounts spent? 1
E2.3 3. Some pupils took part in an obstacle race and their times (in seconds) are recorded below. 23 36 18 29 44 39 36 4 43 41 3 42 3 47 2 36 44 36 22 Draw an ordered stem and leaf diagram to show this information. Key: 2 3 represents 23 seconds............... What was the time taken by the winner? 4. A class of 2 students obtained the following marks in a Mathematics test. 26 18 37 42 29 49 21 2 31 32 1 28 24 3 36 1 31 24 46 41 38 4 16 22 7 Construct a stem and leaf diagram. Place the figures on the leaves in order of size. Using your stem and leaf diagram, or otherwise, find (i) the range, (ii) the median.. The ages of drivers involved in fatal accidents in England during one week are given below. 17 82 4 48 21 3 23 24 18 7 62 4 2 21 33 27 24 37 8 69 6 19 1 21 28 71 43 31 73 26 18 21 34 3 1 63 23 6 22 4 23 27 18 19 32 2 61 36 Illustrate the data using a stem and leaf plot. 16
E2.3 6. The lengths, in seconds, of the tracks on a double album are: Volume 1 23 288 249 21 24 283 266 22 237 221 262 24 23 266 246 273 23 Volume 2 17 18 24 19 22 174 179 182 19 263 19 21 183 21 179 Illustrate the data with a stem and leaf plot with Volume 1 on the left-handside and Volume 2 on the right-hand-side. Compare the two sets of data. E2.4 Graphs: Histograms For continuous data, when any value over a range of values is possible, a frequency graph like the one below should be used, rather than a bar chart which is used for discrete data. 3 Time to complete -mile Charity Fun Run 2 2 1 1 2 3 3 4 4 6 Time (minutes) A graph like this is often called a histogram, and is characterised by having a continuous scale along the horizontal axis. Note that in this case the widths of the bars are all the same, but this is not always the case, as you will see in the next section. Care though must be taken about the end points. For example, the first class interval (in minutes) would normally be 3 time < 3, so that a time of 3 minutes would be in the second class interval. 17
E2.4 A frequency polygon could also be used to show the same data, as on the following graph. Note how it is related to the histogram. 3 Time to complete Charity -mile Fun Run 2 2 1 1 Worked Example 1 Use the data shown on the graphs above to answer these questions. How many people completed the Fun Run in between 4 and 4 minutes? How many people completed the Fun Run in less than 4 minutes? (c) How many people completed the Fun Run in less than 1 hour? Solution (c) 2 3 3 4 4 6 Time (minutes) The 4-4 minute interval contains 21 people. The 3-3 and 3-4 minute intervals must be considered. There are 1 people in the 3-3 minute interval. There are 8 people in the 3-4 minute interval. So there are 1 + 8 = 18 people who complete the run in less than 4 minutes. The number in each interval is needed. So the number of people is: 1 + 8 + 21 + 28 + 7 = 74 Worked Example 2 A group of students measured the reaction times of other students. The times are given below correct to nearest hundredth of a second..44.33.29.49.49.32.46.4.21.16.31.41.29.42.29.47.33.24.43.3.27.31.41.28.41.31.28.22.36.27.4.38.2.24.29.28.29.47.37.28.16.17.31.34.4.26.26.36.27.42 Draw a histogram for this data. 18
E2.4 Solution First the data must be collected into groups, using a tally chart. Reaction Time(s) Tally.1 t <.2 3.2 t <.2 4.2 t <.3 1.3 t <.3.3 t <.4.4 t <.4.4 t <. 9 4 1 Now that the data has been collected in this way, the histogram below can be drawn. 2 1 1.1.1.2.2.3.3.4.4.. Reaction Time (s) Worked Example 3 Draw a frequency polygon for the data on the height of children, given in cm, in the table below. Height (cm) 1 h < 1 1 h <16 16 h < 16 16 h <17 17 h < 17 17 h <18 18 h < 18 4 3 6 8 12 2 Solution Points should be placed above the centre of each interval. The height is given by the frequency. The following graph shows these points. 19
E2.4 1 1 14 1 1 16 16 17 17 18 18 19 Height (cm) Note that points have been placed on the horizontal axis in the intervals that have frequencies of. The points can then be joined to give the frequency polygon below. 1 1 14 1 1 16 16 17 17 18 18 19 Height (cm) Exercises 1. The histogram below shows how the weights of students in a school class were distributed. 2 1 1 4 4 6 6 7 7 8 8 Weight (kg) (c) (d) How many students had a weight greater than 7 kg? How many students had a weight between and 6 kg? How many students had a weight less than kg? How many students were there in that class? 2
E2.4 2. The frequency polygon shows the weekly wages of a large firm. 2 2 1 1 1 1 2 2 3 3 4 4 6 Weekly Weekly Wages Wages ( ) ( ) (c) (d) How many people earn between 3 and 3 per week? How many people earn between 1 and 3 per week? How many people are employed by the firm? What are the largest and smallest possible weekly wages that the graph shows could be paid? 3. An orchard contains 1 apple trees. The weight of apples produced by each tree in one year was recorded. The results are given in the table. Mass of apples (kg) < m 6 6 < m 7 7 < m 8 8 < m 9 9 < m 1 1 < m 11 11 < m 12 12 < m 13 7 13 1 2 22 18 Draw a histogram for the data. 4. A psychologist uses a test in which people have to solve a puzzle. He records the time it took people to solve the puzzle. Time taken (mins) t < 1 1 t < 2 2 t < 3 3 t < 4 4 t < 32 18 7 12 Draw a histogram for the data. 21
E2.4. The finishing times for a cross country race were recorded to the nearest minute. Draw a suitable histogram for the data. 23 27 31 32 32 32 33 34 3 37 38 39 39 4 4 4 41 41 42 42 43 43 43 43 44 44 46 46 46 47 47 48 48 48 1 1 2 3 6. At the end of a football season a newspaper reported the average number of goals scored per match for 1 top footballers. 2.7 1.2 1.3 1.3 2.7 2.1 1.1 1.7 1.8 1.2 1.4 2. 1.4.3 2.2 1.6 2.2 1.4.6 2.2 2.9.6 1.9 1.2.7.7 1.8 2.1 1.9 1.4 1.3 2.2 2.1 2. 1. 1. 1. 2.2 2.6 2.1 2.1 2.2 1.8 1.4 1.6 2. 1.8 1. 1.6 1.2 2.1 2.2.9 1.7 1.4.9 2.6 2.1 2.1.4 2.9 2.7 2.1 2.4 2.7 1.6.2 2.4 2. 2.6 2.1 1.6 2.3 1.9 2. 1.6 1.2. 1.8 1.9 1.7 1.3 1.9 1.7 1.9 1. 1.4.9 1.3.9 3.1 1.9 1.3 1. 2.7 2.6 1.9 1.4 2. 2.1 Use the data given to draw a suitable histogram and then draw a frequency polygon on top of the histogram. 7. The marks gained by a group of students in a mathematics test are shown below. 11 2 24 27 29 34 13 22 26 27 31 36 17 23 26 28 32 38 19 23 27 28 33 39 Copy and complete the following frequency table to show the distribution of the marks. 22
E2.4 Marks 1-14 2 1-19 2-24 2-29 3-34 3-39 3 (c) Draw a histogram to represent the information in the completed frequency table from above. Calculate the probability that a student chosen at random from those who wrote the test scored LESS THAN 2 marks. 8. The age distribution in a town is given in the table. Draw a histogram to show the data. Age a <1 1 a < 2 2 a < 3 3 a < 4 4 a < a < 6 6 a < 7 7 a < 8 8 a < 9 18 1 14 16 12 11 8 1 9. A vehicle hire company owns three types of car which are classified as small, medium and large. The distance travelled by each car is always recorded. Distance (miles) (km) Small Cars Medium Cars Large Cars < t 1 1 < t 2 2 < t 3 3 < t 4 4 < t 8 3 4 12 3 67 16 2 7 24 1 1 12 On the same set of axes draw frequency polygons for each type of car. Comment on the graphs you have drawn. 23
E2.4 1. The graph shows the result of a survey of the times at which students arrived at school one day. 8 6 Number of students Number of pupils 4 2 71 81 72 82 73 83 74 84 7 8 8 9 81 91 Time How many students arrived for school between 73 and 7? 11. The table below gives information about the expected lifetimes, in hours, of 2 light bulbs. Lifetime (t) < t 4 4 < t 8 8 < t 12 12 < t 1616 < t 2 32 6 9 16 6 Mr Jones buys one of the light bulbs. (i) (ii) What is the probability that it will not last more than 4 hours? What is the probability that it will last at least 8 hours but not more than 16 hours? Using axes similar to those below, draw a frequency polygon to illustrate the information in the table. 1 8 6 4 2 4 8 12 16 2 Lifetime (hours) 24
E2.4 12. The height of each of 6 plants of type A was measured and recorded. Height of plant (cm) 8-1 1-12 12-14 14-16 16-18 18-2 2-22 Number of plants 2 3 18 19 18 Draw the frequency polygon of these results on a grid like the one below. 2 1 1 8 1 12 14 16 18 2 22 24 Height (cm) The following graph shows a frequency polygon of 6 plants of type B. 2 1 1 8 1 12 14 16 18 2 22 24 Height (cm) 2
E2.4 Write down two differences between the two types of plant shown by the frequency polygons. E2. Histograms with Unequal Class Intervals When drawing histograms it is possible that the intervals will not have the same width. Consider the data given in the table below. Weight (in grams) w < 4 4 w < w < 6 6 w < 7 7 w < 1 6 8 4 2 The way the data have been presented makes it impossible to draw a histogram with equal class intervals. In order to keep the histogram fair, the area of the bars, rather than the height, must be proportional to the frequency. So on the vertical scale we plot frequency density instead of frequency, where Density Class Width Rewriting the table with an extra column for frequency density, gives = Weight (in grams) Density w < 4.12 4 w < 6.6 w < 6 8.8 6 w < 7 4.4 7 w < 1 2.66... and you can draw the histogram with frequency density on the vertical axis. 26
E2. 1. density. Note 1 2 3 4 6 7 8 9 1 Weight (in grams) You can see that it is the area that is proportional to the frequency in fact, a frequency of 1 is represented by 1 little squares. Worked Example 1 Traffic police recorded the speeds of vehicles passing a speed camera on an open road. Draw a histogram for this data. Solution Speed (km/h) v < v < 6 27 6 v < 7 21 7 v < 7 28 7 v < 8 11 The following table shows how the frequency density can be calculated. Speed (km/h) Class width Density v < v <6 1 27 6 v <7 21 7 v <7 28 7 v <8 11 =.1 27 1 = 1.8 21 28 11 = 4.2 =.6 = 2.2 27
E2. The histogram is shown below. 6 4 density 3 2 1 1 2 3 4 6 7 8 Speed (km/h) Worked Example 2 The histogram below shows the results of a survey into the height of students in a school, 3 Heights of Children students 2 density 1 12 12 13 13 14 14 1 1 16 16 17 17 18 18 19 Heights Height (cm) find the number of students with heights between: (i) 12 and 14 cm, (ii) 17 and 17 cm. find the total number of students measured. Solution (i) For the 12 to 14 cm interval: Density Class Width = = 12. 2 = 2 1. 2 = 24 students 28
E2. (ii) For the 17 to 17 cm interval: Density Class Width = = 24. = 2. 4 = 12 students To find the total, the numbers in each class interval must be found and added together. Total = 2 12. + 1 18. + 1 22. + 28. + 24. + 18. + 1 11. Exercises = 24 + 18 + 33 + 14 + 12 + 9 + 11 = 121 1. For a project in Biology, Sharma gathered data on the length of leaves from a tree and drew the histogram below. 3. density 2. Lengths of leaves 1. 1 2 3 4 6 7 8 9 1 11 12 Length (cm) (c) How many leaves had a length less than 6 cm? How many leaves had a length greater than 9 cm? How many leaves did she measure? 2. Jennifer collected data on the length of time it took her to travel to school. She drew the histogram below. 2 Time taken to travel to school density 1 1 1 2 2 3 Time taken (mins) This histogram contains an error. What is it? 29
E2. 3. A teacher recorded all the scores of the students who took a maths test in his school. These scores are summarised in the table below. Score t < 3 3 t < 4 4 t < t < 7 7 t 1 3 7 2 42 16 Draw a histogram for this data. 4. The distribution of the ages of inhabitants of a village is shown in the table below. Age - 4-9 1-19 2-39 4-9 6-64 6-79 8-99 1 12 19 36 3 9 11 3 Explain why the width of the first class interval is. (c) Find the width of all the other class intervals. Draw a histogram to show this data.. The finishing times to the nearest minute for the competitors in a half-marathon to complete the race are given below. Group the data into suitable intervals and draw a histogram. 13 17 127 22 1 12 169 16 122 13 13 117 9 113 98 93 112 121 98 136 123 126 134 17 137 116 163 176 96 123 116 117 11 1 11 92 124 1 118 8 177 16 21 132 129 12 11 84 13 17 11 133 11 1 117 97 143 114 112 19 3
E2. 6. The age of each person at a party is illustrated in the histogram below. density 1 2 3 4 6 7 8 9 1 Age There are 6 people in the 7-8 age range. How many people are there in the 4- age range? How many people are there in the -7 age range? 7. A sample was taken of the telephone calls to a school switchboard. The lengths of the telephone calls are recorded, in minutes, in this table. Time in minutes (t) < t 1 1< t 3 3 < t < t 1 1 < t 2 Number of calls 12 32 19 2 1 Copy and complete the histogram to show this information. 2 per 1 minute interval 1 1 1 1 2 Time in minutes (t) 31
E2. 8. The following histogram below represents the number of spectators at professional football matches in England one Saturday. Density 1 2 3 4 Attendance No match had more than 4 spectators. At 4 matches the number of spectators was greater than or equal to 1 and less than 1. Use the information in the histogram to complete a copy of the following frequency table. 32
E2. Number of spectators (n) n < 3 3 n < n < 1 1 n < 1 1 n < 3 3 n < 4 4 Calculate the total number of professional football matches played in England on that Saturday. 33